- The iPod does not have the necessary BT profiles to pair usefully with a computer. It may pair but you can't do anything.
- The car system may require a BT profile not on the 2G iPod. The car system may use the Hand Free Profile that only the 4G and later, support
The above link lists what profile the iPod supports. Does the care system use one of the one supported by the 2G?
The 2G supports A2DP but not HFP. A2DP is used for streaming so yo may be able to stream music from the iPod to the car system. However, HFP is typically uses with headsets that have to transmit to another device (iPhone). The lack of HFP support is likely what is causing the car system not to work with the iPod.